Our sky looks blue because the molecules in the air scatter the white light coming from the sun, and the blue light is scattered more than red light.
But in space, there is no air, so none of the light coming from the stars gets scattered. We see bright points of light of the stars. but everything else inbetween is empty – nothing to scatter the light, so it looks black. 🙂
– Leila Battison answered on 23 Mar 2012: http://spacem12.imascientist.org.uk/2012/03/why-does-space-look-black